From the above derivation, we can observe that the cascaded channel \(\mathbf {h}\)  is the sum of \(L\)  2D frequency components, which has a sparse representation in the 2D Fourier dictionary since \(L\ll N\) .
To represent \(\mathbf {h}\)  in a sparse form, a conventional approach is to discretize the angular domain into a grid and form a 2D discrete Fourier transform (DFT) dictionary [1]}.
However, this approach incurs off-grid error since frequency components (AOAs/AoDs) do not lie exactly on the grid, and hence the performance of sparse recovery algorithms may degrade considerably [2]}.
Although increasing the grid density can alleviate the off-grid problem to a certain extent, the computational complexity also increases dramatically, especially under the 2D setting.
To bypass this issue, we adopt the atomic norm as the sparsity promoter of the cascaded channel, which does not discretize the angular domain and thus no off-grid error will be induced.
A comprehensive survey on the atomic norm can be found in [3]}.
